## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 2013

For a sequence { om } satisfying ( 3 ) , A is

consists precisely of those o for which the limit in ( 9 ) exists . Our next concern

will be with the question of the existence of a resolution of the identity for A . This

leads ...

For a sequence { om } satisfying ( 3 ) , A is

**given**by ( 9 ) and the domain of Aconsists precisely of those o for which the limit in ( 9 ) exists . Our next concern

will be with the question of the existence of a resolution of the identity for A . This

leads ...

Page 2096

A proof similar to the one

A version of the canonical reduction for everywhere defined spectral operators in

a locally convex linear space was

A proof similar to the one

**given**here was communicated to the authors by Foiaş .A version of the canonical reduction for everywhere defined spectral operators in

a locally convex linear space was

**given**by Ionescu Tulcea [ 3 ] when the space ...Page 2376

Applications of this same method to other operators are

Section 5 . In Section 3 we generalize the Friedrichs technique to operators with

discrete spectra , along lines first developed by Turner . Here one begins with an

...

Applications of this same method to other operators are

**given**as exercises inSection 5 . In Section 3 we generalize the Friedrichs technique to operators with

discrete spectra , along lines first developed by Turner . Here one begins with an

...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero